Had guy drop his mini in a random ally and he is telling me that it's a 24 hours delay. Here is the pic he sent just now.
Yeah, you’ll be able to claim rewards after the 24-hour qualifying timer once you switch. The only catch is you won’t get the milestones your new alliance hit before you joined, but anything they hit after you’re in will be claimable for you.
I switched alliances recently too, moved from Tier 3 to Tier 2, and it worked just like that. No issues at all.